Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
2072 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 2072 conjugacy classes of subgroups — too many to draw. Only its 85 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C34×C37⋊C3 | C3 | semidirect |
| 2. C3×#15688512 | C3 | semidirect |
| 3. #22582554 | C3 | semidirect |
| 4. C37×C32⋊H(3,𝔽3) | C3 | semidirect |
| 9. C3×#11758608 | C32 | semidirect |
| 14. C3×H(3,𝔽3)×C37 | C32 | semidirect |
| 27. C32×C37⋊C3 | H(3,𝔽3) | semidirect |
| 39. C32×C37 | AΣL(1,𝔽27) | semidirect |
| 51. C32⋊H(3,𝔽3) | C37⋊C3 | semidirect |
| 65. C3×H(3,𝔽3) | C3×C37⋊C3 | semidirect |
| 68. C37 | #10624730 | semidirect |
| 97. C32 | #15688512 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C34×C37⋊C3 | 3 |
| C3×#15688512 | 3 |
| #22582554 | 3 |
| C37×C32⋊H(3,𝔽3) | 3 |
| #10624730 | 37 |